Question
In: Physics
A) A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released...
A)
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass id riven by an external force equal to f(t) = 20 cos 3t use g=32 ft/s^2 for the acceleration due to gravity)
B)
A mass of 1 slug, when attached to a spring stretches it 2 feet and then comes to rest in the equilibrium position starting at t=0 an external force equal to f(t)=6 sin 4t is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. use g=32 ft/s^2 for the acceleration due to gravity.
Solutions
genius_generous answered 1 year agoRelated Solutions
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring
8
3
feet. The mass is initially released from rest from a point 7
feet below the equilibrium position, and the subsequent motion
takes place in a medium that offers a damping force that is
numerically equal to
1
2
the instantaneous velocity. Find the equation of motion
x(t)
if the mass is driven by an external force equal to
f(t) = 25
cos(3t).
(Use
g = 32 ft/s2
for the acceleration...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass
is initially released from rest from a point 7 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 1 2
the instantaneous velocity. Find the equation of motion x(t) if the
mass is driven by an external force equal to f(t) = 25 cos 3t. (Use
g = 32 ft/s2 for the...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16
pounds stretches a spring
8
3
feet. The mass is
initially released from rest from a point 5 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to
1
2
the instantaneous
velocity. Find the equation of motion
x(t)
if the mass is driven
by an external force equal to
f(t)
= 20 cos(3t).
(Use
g = 32
ft/s2
for the acceleration...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3
feet. The mass is initially released from rest from a point 3 feet
below the equilibrium position, and the subsequent motion takes
place in a medium that offers a damping force that is numerically
equal to 1/2
the instantaneous velocity. Find the equation of motion x(t)
if the mass is driven by an external force equal to f(t) = 10
cos(3t).
(Use g = 32 ft/s2
for the acceleration due to...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass
is initially released from rest from a point 5 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 1/2
the instantaneous velocity. Find the equation of motion x(t) if the
mass is driven by an external force equal to f(t) = 20 cos(3t).
(Use g = 32 ft/s2 for the acceleration due to...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass
is initially released from rest from a point 2 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 1/2
the instantaneous velocity.
Find the equation of motion x(t) if the mass is driven by an
external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for
the acceleration due to...
A mass weighing 32 pounds stretches a spring 16 feet. The mass is initially released from...
A
mass weighing 32 pounds stretches a spring 16 feet. The mass is
initially released from rest from a point 2 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 1/2
the instantaneous velocity. Find the equation of motion if the mass
is driven by an external force equal to f(t)=10cos(3t).
A mass weighing 12 pounds stretches a spring 2 feet. The mass is initially released from...
A mass weighing 12 pounds stretches a spring 2 feet. The mass is
initially released from a point 1 foot below equilibrium with an
upward velocity of 4 ft/s.
(a) Find the equation of motion
(b) In correct units, what are the amplitude, period, and
frequency of this simple harmonic motion?
(c) What is the velocity of the mass at ? = 3? 16 seconds?
(d) Find the first three times that the velocity is zero,
expressed both in exact...
A mass weighing 8 pounds stretches a spring 1 foot. The mass is initially released from...
A mass weighing 8 pounds stretches a spring 1 foot. The mass is
initially released from rest from a point 2 feet below the
equilibrium position, and the subsequent motion takes place in a
medium that offers a damping force that is numerically equal to 2
times the instantaneous velocity. Find the equation of motion
(solve the IVP) if the mass is driven by an external force equal to
f(t) = 5 cos(2t).
Graph the solution. What part of the...
A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from...
A mass weighing 20 pounds stretches a spring 6 inches. The mass
is initially released from rest from a point 8 inches below the
equilibrium position.
(a) Find the position x of the mass at the times
t = π/12, π/8, π/6,
π/4, and 9π/32 s.
(Use
g = 32 ft/s2
for the acceleration due to gravity.)
x(π/12)
=
−14
ft
x(π/8)
=
−.5
ft
x(π/6)
=
−0.25
ft
x(π/4)
=
0.5
ft
x(9π/32)
=
0.35
ft
(b) What is...
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